Actual source code: ex62.c
1: static char help[] = "Illustrates use of PCGASM.\n\
2: The Generalized Additive Schwarz Method for solving a linear system in parallel with KSP. The\n\
3: code indicates the procedure for setting user-defined subdomains.\n\
4: See section 'ex62' below for command-line options.\n\
5: Without -user_set_subdomains, the general PCGASM options are meaningful:\n\
6: -pc_gasm_total_subdomains\n\
7: -pc_gasm_print_subdomains\n\
8: \n";
10: /*
11: Note: This example focuses on setting the subdomains for the GASM
12: preconditioner for a problem on a 2D rectangular grid. See ex1.c
13: and ex2.c for more detailed comments on the basic usage of KSP
14: (including working with matrices and vectors).
16: The GASM preconditioner is fully parallel. The user-space routine
17: CreateSubdomains2D that computes the domain decomposition is also parallel
18: and attempts to generate both subdomains straddling processors and multiple
19: domains per processor.
21: This matrix in this linear system arises from the discretized Laplacian,
22: and thus is not very interesting in terms of experimenting with variants
23: of the GASM preconditioner.
24: */
26: /*
27: Include "petscksp.h" so that we can use KSP solvers. Note that this file
28: automatically includes:
29: petscsys.h - base PETSc routines petscvec.h - vectors
30: petscmat.h - matrices
31: petscis.h - index sets petscksp.h - Krylov subspace methods
32: petscviewer.h - viewers petscpc.h - preconditioners
33: */
34: #include <petscksp.h>
36: PetscErrorCode AssembleMatrix(Mat,PetscInt m,PetscInt n);
38: int main(int argc,char **args)
39: {
40: Vec x,b,u; /* approx solution, RHS, exact solution */
41: Mat A; /* linear system matrix */
42: KSP ksp; /* linear solver context */
43: PC pc; /* PC context */
44: IS *inneris,*outeris; /* array of index sets that define the subdomains */
45: PetscInt overlap; /* width of subdomain overlap */
46: PetscInt Nsub; /* number of subdomains */
47: PetscInt m,n; /* mesh dimensions in x- and y- directions */
48: PetscInt M,N; /* number of subdomains in x- and y- directions */
50: PetscMPIInt size;
51: PetscBool flg=PETSC_FALSE;
52: PetscBool user_set_subdomains=PETSC_FALSE;
53: PetscReal one,e;
55: PetscInitialize(&argc,&args,(char*)0,help);
56: MPI_Comm_size(PETSC_COMM_WORLD,&size);
57: PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"ex62","PCGASM");
58: m = 15;
59: PetscOptionsInt("-M", "Number of mesh points in the x-direction","PCGASMCreateSubdomains2D",m,&m,NULL);
60: n = 17;
61: PetscOptionsInt("-N","Number of mesh points in the y-direction","PCGASMCreateSubdomains2D",n,&n,NULL);
62: user_set_subdomains = PETSC_FALSE;
63: PetscOptionsBool("-user_set_subdomains","Use the user-specified 2D tiling of mesh by subdomains","PCGASMCreateSubdomains2D",user_set_subdomains,&user_set_subdomains,NULL);
64: M = 2;
65: PetscOptionsInt("-Mdomains","Number of subdomain tiles in the x-direction","PCGASMSetSubdomains2D",M,&M,NULL);
66: N = 1;
67: PetscOptionsInt("-Ndomains","Number of subdomain tiles in the y-direction","PCGASMSetSubdomains2D",N,&N,NULL);
68: overlap = 1;
69: PetscOptionsInt("-overlap","Size of tile overlap.","PCGASMSetSubdomains2D",overlap,&overlap,NULL);
70: PetscOptionsEnd();
72: /* -------------------------------------------------------------------
73: Compute the matrix and right-hand-side vector that define
74: the linear system, Ax = b.
75: ------------------------------------------------------------------- */
77: /*
78: Assemble the matrix for the five point stencil, YET AGAIN
79: */
80: MatCreate(PETSC_COMM_WORLD,&A);
81: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
82: MatSetFromOptions(A);
83: MatSetUp(A);
84: MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);
85: MatSetOption(A, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_FALSE);
86: AssembleMatrix(A,m,n);
88: /*
89: Create and set vectors
90: */
91: VecCreate(PETSC_COMM_WORLD,&b);
92: VecSetSizes(b,PETSC_DECIDE,m*n);
93: VecSetFromOptions(b);
94: VecDuplicate(b,&u);
95: VecDuplicate(b,&x);
96: one = 1.0;
97: VecSet(u,one);
98: MatMult(A,u,b);
100: /*
101: Create linear solver context
102: */
103: KSPCreate(PETSC_COMM_WORLD,&ksp);
105: /*
106: Set operators. Here the matrix that defines the linear system
107: also serves as the preconditioning matrix.
108: */
109: KSPSetOperators(ksp,A,A);
111: /*
112: Set the default preconditioner for this program to be GASM
113: */
114: KSPGetPC(ksp,&pc);
115: PCSetType(pc,PCGASM);
117: /* -------------------------------------------------------------------
118: Define the problem decomposition
119: ------------------------------------------------------------------- */
121: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
122: Basic method, should be sufficient for the needs of many users.
123: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
125: Set the overlap, using the default PETSc decomposition via
126: PCGASMSetOverlap(pc,overlap);
127: Could instead use the option -pc_gasm_overlap <ovl>
129: Set the total number of blocks via -pc_gasm_blocks <blks>
130: Note: The GASM default is to use 1 block per processor. To
131: experiment on a single processor with various overlaps, you
132: must specify use of multiple blocks!
133: */
135: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
136: More advanced method, setting user-defined subdomains
137: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
139: Firstly, create index sets that define the subdomains. The utility
140: routine PCGASMCreateSubdomains2D() is a simple example, which partitions
141: the 2D grid into MxN subdomains with an optional overlap.
142: More generally, the user should write a custom routine for a particular
143: problem geometry.
145: Then call PCGASMSetLocalSubdomains() with resulting index sets
146: to set the subdomains for the GASM preconditioner.
147: */
149: if (user_set_subdomains) { /* user-control version */
150: PCGASMCreateSubdomains2D(pc, m,n,M,N,1,overlap,&Nsub,&inneris,&outeris);
151: PCGASMSetSubdomains(pc,Nsub,inneris,outeris);
152: PCGASMDestroySubdomains(Nsub,&inneris,&outeris);
153: flg = PETSC_FALSE;
154: PetscOptionsGetBool(NULL,NULL,"-subdomain_view",&flg,NULL);
155: if (flg) {
156: PetscInt i;
157: PetscPrintf(PETSC_COMM_SELF,"Nmesh points: %D x %D; subdomain partition: %D x %D; overlap: %D; Nsub: %D\n",m,n,M,N,overlap,Nsub);
158: PetscPrintf(PETSC_COMM_SELF,"Outer IS:\n");
159: for (i=0; i<Nsub; i++) {
160: PetscPrintf(PETSC_COMM_SELF," outer IS[%D]\n",i);
161: ISView(outeris[i],PETSC_VIEWER_STDOUT_SELF);
162: }
163: PetscPrintf(PETSC_COMM_SELF,"Inner IS:\n");
164: for (i=0; i<Nsub; i++) {
165: PetscPrintf(PETSC_COMM_SELF," inner IS[%D]\n",i);
166: ISView(inneris[i],PETSC_VIEWER_STDOUT_SELF);
167: }
168: }
169: } else { /* basic setup */
170: KSPSetFromOptions(ksp);
171: }
173: /* -------------------------------------------------------------------
174: Set the linear solvers for the subblocks
175: ------------------------------------------------------------------- */
177: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
178: Basic method, should be sufficient for the needs of most users.
179: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
181: By default, the GASM preconditioner uses the same solver on each
182: block of the problem. To set the same solver options on all blocks,
183: use the prefix -sub before the usual PC and KSP options, e.g.,
184: -sub_pc_type <pc> -sub_ksp_type <ksp> -sub_ksp_rtol 1.e-4
186: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
187: Advanced method, setting different solvers for various blocks.
188: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
190: Note that each block's KSP context is completely independent of
191: the others, and the full range of uniprocessor KSP options is
192: available for each block.
194: - Use PCGASMGetSubKSP() to extract the array of KSP contexts for
195: the local blocks.
196: - See ex7.c for a simple example of setting different linear solvers
197: for the individual blocks for the block Jacobi method (which is
198: equivalent to the GASM method with zero overlap).
199: */
201: flg = PETSC_FALSE;
202: PetscOptionsGetBool(NULL,NULL,"-user_set_subdomain_solvers",&flg,NULL);
203: if (flg) {
204: KSP *subksp; /* array of KSP contexts for local subblocks */
205: PetscInt i,nlocal,first; /* number of local subblocks, first local subblock */
206: PC subpc; /* PC context for subblock */
207: PetscBool isasm;
209: PetscPrintf(PETSC_COMM_WORLD,"User explicitly sets subdomain solvers.\n");
211: /*
212: Set runtime options
213: */
214: KSPSetFromOptions(ksp);
216: /*
217: Flag an error if PCTYPE is changed from the runtime options
218: */
219: PetscObjectTypeCompare((PetscObject)pc,PCGASM,&isasm);
222: /*
223: Call KSPSetUp() to set the block Jacobi data structures (including
224: creation of an internal KSP context for each block).
226: Note: KSPSetUp() MUST be called before PCGASMGetSubKSP().
227: */
228: KSPSetUp(ksp);
230: /*
231: Extract the array of KSP contexts for the local blocks
232: */
233: PCGASMGetSubKSP(pc,&nlocal,&first,&subksp);
235: /*
236: Loop over the local blocks, setting various KSP options
237: for each block.
238: */
239: for (i=0; i<nlocal; i++) {
240: KSPGetPC(subksp[i],&subpc);
241: PCSetType(subpc,PCILU);
242: KSPSetType(subksp[i],KSPGMRES);
243: KSPSetTolerances(subksp[i],1.e-7,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
244: }
245: } else {
246: /*
247: Set runtime options
248: */
249: KSPSetFromOptions(ksp);
250: }
252: /* -------------------------------------------------------------------
253: Solve the linear system
254: ------------------------------------------------------------------- */
256: KSPSolve(ksp,b,x);
258: /* -------------------------------------------------------------------
259: Assemble the matrix again to test repeated setup and solves.
260: ------------------------------------------------------------------- */
262: AssembleMatrix(A,m,n);
263: KSPSolve(ksp,b,x);
265: /* -------------------------------------------------------------------
266: Compare result to the exact solution
267: ------------------------------------------------------------------- */
268: VecAXPY(x,-1.0,u);
269: VecNorm(x,NORM_INFINITY, &e);
271: flg = PETSC_FALSE;
272: PetscOptionsGetBool(NULL,NULL,"-print_error",&flg,NULL);
273: if (flg) {
274: PetscPrintf(PETSC_COMM_WORLD, "Infinity norm of the error: %g\n", (double)e);
275: }
277: /*
278: Free work space. All PETSc objects should be destroyed when they
279: are no longer needed.
280: */
282: KSPDestroy(&ksp);
283: VecDestroy(&u);
284: VecDestroy(&x);
285: VecDestroy(&b);
286: MatDestroy(&A);
287: PetscFinalize();
288: return 0;
289: }
291: PetscErrorCode AssembleMatrix(Mat A,PetscInt m,PetscInt n)
292: {
293: PetscInt i,j,Ii,J,Istart,Iend;
294: PetscScalar v;
296: MatGetOwnershipRange(A,&Istart,&Iend);
297: for (Ii=Istart; Ii<Iend; Ii++) {
298: v = -1.0; i = Ii/n; j = Ii - i*n;
299: if (i>0) {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
300: if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
301: if (j>0) {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
302: if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
303: v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);
304: }
305: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
306: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
308: return 0;
309: }
311: /*TEST
313: test:
314: suffix: 2D_1
315: args: -M 7 -N 9 -user_set_subdomains -Mdomains 1 -Ndomains 3 -overlap 1 -print_error -pc_gasm_print_subdomains
317: test:
318: suffix: 2D_2
319: nsize: 2
320: args: -M 7 -N 9 -user_set_subdomains -Mdomains 1 -Ndomains 3 -overlap 1 -print_error -pc_gasm_print_subdomains
322: test:
323: suffix: 2D_3
324: nsize: 3
325: args: -M 7 -N 9 -user_set_subdomains -Mdomains 1 -Ndomains 3 -overlap 1 -print_error -pc_gasm_print_subdomains
327: test:
328: suffix: hp
329: nsize: 4
330: requires: superlu_dist
331: args: -M 7 -N 9 -pc_gasm_overlap 1 -sub_pc_type lu -sub_pc_factor_mat_solver_type superlu_dist -ksp_monitor -print_error -pc_gasm_total_subdomains 2 -pc_gasm_use_hierachical_partitioning 1
332: output_file: output/ex62.out
333: TODO: bug, triggers New nonzero at (0,15) caused a malloc in MatCreateSubMatrices_MPIAIJ_SingleIS_Local
335: test:
336: suffix: superlu_dist_1
337: requires: superlu_dist
338: args: -M 7 -N 9 -print_error -pc_gasm_total_subdomains 1 -pc_gasm_print_subdomains -sub_pc_type lu -sub_pc_factor_mat_solver_type superlu_dist
340: test:
341: suffix: superlu_dist_2
342: nsize: 2
343: requires: superlu_dist
344: args: -M 7 -N 9 -print_error -pc_gasm_total_subdomains 1 -pc_gasm_print_subdomains -sub_pc_type lu -sub_pc_factor_mat_solver_type superlu_dist
346: test:
347: suffix: superlu_dist_3
348: nsize: 3
349: requires: superlu_dist
350: args: -M 7 -N 9 -print_error -pc_gasm_total_subdomains 2 -pc_gasm_print_subdomains -sub_pc_type lu -sub_pc_factor_mat_solver_type superlu_dist
352: test:
353: suffix: superlu_dist_4
354: nsize: 4
355: requires: superlu_dist
356: args: -M 7 -N 9 -print_error -pc_gasm_total_subdomains 2 -pc_gasm_print_subdomains -sub_pc_type lu -sub_pc_factor_mat_solver_type superlu_dist
358: TEST*/